Finite Group Databasebeta

← #14763594

Subgroups — #14763594

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623025C211yesmaximal, characteristic
2#13071214C211yesmaximal, characteristic, complemented
3#13069600C212yesmaximal, complemented
4#13069451C212yesmaximal, complemented
5#13069069C214yesmaximal, complemented
6#13068601C214yesmaximal, complemented
7C11×#2315C211yesmaximal, characteristic, complemented
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2211yescharacteristic
10C2×#67006C2212yes—
11C2×#66983C2211yescharacteristic
12C2×C4×C22⋊D11C2212yes—
13C2×#66977C2211yescharacteristic
14#10623025—24no—
15#10623025—24no—
16C2×#66938C412yescomplemented
17C2×#66937C412yescomplemented
18C2×#66936C412yescomplemented
19C2×#66932C412yescomplemented
20C11×#385—24no—
21C11×#380C2212yes—
22C11×#380C2212yes—
23#10622860C2212yes—
24#10622825C2212yes—
25C4×C22⋊Dic11C2212yes—
26C2×#66870C2218yes—
27#10622564—24no—
28#10622165C2218yes—
29C25×C11C2311yescharacteristic
30C23×C4×C11—22no—
31C23×C4×C11C2311yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11C2×C412yes—
34C22×C22⋊D11C2×C412yes—
35C22×C22⋊D11C2312yes—
36C22×D44C2×C411yescharacteristic, complemented
37C22×C4×D11C2×C412yescomplemented
38C22×Dic22C2×C411yescharacteristic, complemented
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—44no—
43C2×C11×C22⋊C4C2×C412yes—
44C2×C11×C22⋊C4C2×C412yes—
45C2×C11×C22⋊C4D414yes—
46C2×C11×C22⋊C4D414yes—
47C2×C11×C22⋊C4C2314yes—
48#67006—24no—
49#67006—24no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11C2×C412yes—
53C2×C22⋊Dic11C2×C412yes—
54C2×C22⋊Dic11C2314yes—
55C2×C22⋊Dic11C2312yes—
56#66983—22no—
57#66983—22no—
58C4×C22⋊D11—24no—
59C4×C22⋊D11—24no—
60C2×(C2×D11)⋊C4C2×C412yescomplemented
61C2×(C2×D11)⋊C4C2×C412yescomplemented
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11C2×C411yescharacteristic, complemented
64C2×C4⋊Dic11C2×C411yescharacteristic, complemented
65#66977—22no—
66#66977—22no—
67C2×Dic11⋊C4C2×C412yescomplemented
68C2×Dic11⋊C4C2×C412yescomplemented
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2×C412yescomplemented
71#66938—28no—
72#66937—28no—
73#66936—28no—
74#66932—28no—
75C11×#95—22no—
76C11×#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79#66870—48no—
80#21876—111nomaximal, Sylow
81C24×C11—22no—
82C24×C11—22no—
83C24×C11—81no—
84C24×C11—81no—
85C24×C11C22×C412yes—
86C24×C11C2×D412yes—
87C24×C11C2×D412yes—
88C24×C11C2411yescharacteristic
89C23×D11C22×C412yes—
90C22×C4×C11—24no—
91C22×C4×C11—44no—
92C22×C4×C11—81no—
93C22×C4×C11—81no—
94C22×C4×C11—82no—
95C22×C4×C11—82no—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C2×C22⋊D11—24no—
104C2×C22⋊D11—24no—
105C2×C22⋊D11—22no—
106C2×C22⋊D11—22no—
107C2×C22⋊D11—24no—
108C2×C22⋊D11—24no—
109C2×C22⋊D11—82no—
110C2×C22⋊D11—82no—
111C22×Dic11—24no—
112C22×Dic11C22×C412yes—
113C22×Dic11C22×C412yes—
114C22×Dic11C22×C412yes—
115C2×D44—22no—
116C2×D44—81no—
117C2×C4×D11—24no—
118C2×C4×D11—82no—
119C2×Dic22—22no—
120C2×Dic22—81no—
121C11×C4⋊C4—82no—
122C11×C4⋊C4—82no—
123C11×C22⋊C4—28no—
124C11×C22⋊C4—44no—
125C11×C22⋊C4C22⋊C418yes—
126C11×C22⋊C4C22⋊C418yes—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—22no—
130C22⋊Dic11—22no—
131C22⋊Dic11—24no—
132C22⋊Dic11—24no—
133C22⋊Dic11—82no—
134C22⋊Dic11—82no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—24no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—82no—
140Dic11⋊C4—24no—
141Dic11⋊C4—24no—
142C4×Dic11—24no—
143C4×Dic11—82no—
144C2×#538—111no—
145#2315D1111yescharacteristic, complemented
146#2312—111no—
147#1996—112no—
148#1964—112no—
149#1898—114no—
150#1799—114no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—24no—
154C23×C11—24no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—84no—
164C23×C11—84no—
165C23×C11C2×C22⋊C414yes—
166C23×C11C23×C411yescharacteristic
167C23×C11C22×D411yescharacteristic
168C23×C11C22×D411yescharacteristic
169C23×C11H(5,𝔽2)12yes—
170C23×C112−1+412yes—
171C22×D11—22no—
172C22×D11—24no—
173C22×D11—42no—
174C22×D11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11—88no—
186C2×C4×C11C2×C22⋊C414yes—
187C2×C4×C11C2×C22⋊C412yes—
188C2×C4×C11C2×C22⋊C412yes—
189C22⋊D11—42no—
190C22⋊D11—42no—
191C22⋊D11—44no—
192C22⋊D11—84no—
193C22⋊D11—84no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—24no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—44no—
201C2×Dic11—44no—
202C2×Dic11—44no—
203D44—82no—
204C4×D11—84no—
205Dic22—82no—
206#538—224no—
207#538—224no—
208C2×#126—112no—
209C2×#124—112no—
210C2×#123—112no—
211C2×C22⋊Q8—111no—
212C2×#121—111no—
213C2×#121—112no—
214C2×#120—112no—
215C2×C4×D4—112no—
216C22×C22⋊C4C2×D1112yes—
217C22×C22⋊C4C2×D1111yescharacteristic
218C2×#99—118no—
219#388—224no—
220#385—24no—
221#380—112no—
222#380C2×D1112yes—
223#380C2×D1112yes—
224#379—112no—
225C4×C22⋊C4—112no—
226#342—118no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—24no—
234C22×C11—24no—
235C22×C11—24no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—44no—
239C22×C11—44no—
240C22×C11—84no—
241C22×C11—84no—
242C22×C11C22×C22⋊C411yescharacteristic
243C22×C11#52012yes—
244C22×C11#53511yescharacteristic
245C22×C11#53611yescharacteristic
246C22×C11#53712yes—
247C2×D11—42no—
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—84no—
251C4×C11—22no—
252C4×C11—24no—
253C4×C11—22no—
254C4×C11—84no—
255Dic11—42no—
256Dic11—42no—
257Dic11—42no—
258Dic11—84no—
259C25C22×D1111yescharacteristic
260C22×Q8—111no—
261C22×D4—112no—
262C22×D4—112no—
263C22×D4—112no—
264C22×D4—111no—
265C23×C4—22no—
266C23×C4—112no—
267C23×C4C22×D1111yescharacteristic
268C23×C4C22×D1111yescharacteristic
269#126—228no—
270#124—228no—
271#123—228no—
272C22⋊Q8—222no—
273C22⋊Q8—222no—
274#121—222no—
275#121—222no—
276#121—228no—
277#120—224no—
278#120—224no—
279C4×D4—224no—
280C4×D4—224no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—222no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—44no—
290C2×C22⋊C4—112no—
291C2×C22⋊C4—112no—
292C2×C22⋊C4—112no—
293C2×C22⋊C4—112no—
294C2×C22⋊C4—112no—
295C2×C22⋊C4—114no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4C4×D1112yes—
299C2×C22⋊C4C4×D1112yes—
300C2×C22⋊C4D4414yes—
301C2×C22⋊C4C22⋊D1114yes—
302C2×C22⋊C4C22×D1114yes—
303C2×C42—112no—
304C2×C42—222no—
305#99—448no—
306#95—22no—
307#95—22no—
308#95—222no—
309#95—222no—
310C2×C11—22no—
311C2×C11—21no—
312C2×C11—22no—
313C2×C11—21no—
314C2×C11—44no—
315C2×C11#231111yescharacteristic
316C2×C11#288311yescharacteristic
317C2×C11#288311yescharacteristic
318D11—82no—
319C24—22no—
320C24—22no—
321C24—81no—
322C24—81no—
323C24—112no—
324C24C2×C4×D1112yes—
325C24C2×D4412yes—
326C24C2×C22⋊D1112yes—
327C24C23×D1111yescharacteristic
328C2×Q8—222no—
329C2×Q8—881no—
330C2×D4—222no—
331C2×D4—224no—
332C2×D4—224no—
333C2×D4—222no—
334C2×D4—224no—
335C2×D4—224no—
336C2×D4—222no—
337C2×D4—881no—
338C2×D4—882no—
339C2×D4—882no—
340C22×C4—24no—
341C22×C4—44no—
342C22×C4—81no—
343C22×C4—81no—
344C22×C4—82no—
345C22×C4—82no—
346C22×C4—112no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—224no—
350C22×C4—224no—
351C22×C4—882no—
352C22×C4C2×C4×D1112yes—
353C22×C4C2×C4×D1111yescharacteristic
354C22×C4C2×C4×D1111yescharacteristic
355C22×C4C2×D4412yes—
356C22×C4C2×D4412yes—
357C22×C4C2×C22⋊D1112yes—
358C22×C4C2×C22⋊D1112yes—
359C4⋊C4—82no—
360C4⋊C4—82no—
361C4⋊C4—224no—
362C4⋊C4—224no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—882no—
366C22⋊C4—28no—
367C22⋊C4—44no—
368C22⋊C4—224no—
369C22⋊C4—224no—
370C22⋊C4—222no—
371C22⋊C4—222no—
372C22⋊C4—224no—
373C22⋊C4—224no—
374C22⋊C4—224no—
375C22⋊C4—224no—
376C22⋊C4—882no—
377C22⋊C4—882no—
378C22⋊C4(C2×D11)⋊C418yes—
379C22⋊C4(C2×D11)⋊C418yes—
380C42—224no—
381C42—882no—
382C11#2187611yescharacteristic, complemented, Sylow
383C23—22no—
384C23—22no—
385C23—24no—
386C23—24no—
387C23—42no—
388C23—42no—
389C23—41no—
390C23—41no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—84no—
396C23—84no—
397C23—222no—
398C23—224no—
399C23—442no—
400C23—442no—
401C23C2×(C2×D11)⋊C414yes—
402C23C22×C4×D1111yescharacteristic
403C23C22×D4411yescharacteristic
404C23#6703712yes—
405C23#6704012yes—
406C23C22×C22⋊D1111yescharacteristic
407Q8—882no—
408D4—444no—
409D4—442no—
410D4—442no—
411D4—882no—
412D4—884no—
413D4—884no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—88no—
425C2×C4—224no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—444no—
432C2×C4—444no—
433C2×C4—444no—
434C2×C4—884no—
435C2×C4C2×(C2×D11)⋊C414yes—
436C2×C4C2×(C2×D11)⋊C412yes—
437C2×C4C2×(C2×D11)⋊C412yes—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—24no—
445C22—24no—
446C22—24no—
447C22—42no—
448C22—42no—
449C22—44no—
450C22—44no—
451C22—84no—
452C22—84no—
453C22—442no—
454C22—442no—
455C22—442no—
456C22—884no—
457C22#1062303512yes—
458C22#1062304112yes—
459C22C22×(C2×D11)⋊C411yescharacteristic
460C22#1062333611yescharacteristic
461C22#1062334711yescharacteristic
462C4—24no—
463C4—22no—
464C4—22no—
465C4—84no—
466C4—442no—
467C4—442no—
468C4—442no—
469C4—884no—
470C2—21no—
471C2—22no—
472C2—21no—
473C2—22no—
474C2—44no—
475C2—882no—
476C2#1307120911yescharacteristic
477C2#1307707611yescharacteristic
478C2#1307707611yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2315C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623025C2
cosocleC24×C11C24
hypercenter#2315D11
hypocenterC11#21876
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ #2315

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13071214C2semidirect
3. #13069600C2semidirect
4. #13069451C2semidirect
5. #13069069C2semidirect
6. #13068601C2semidirect
7. C11×#2315C2semidirect
16. C2×#66938C4semidirect
17. C2×#66937C4semidirect
18. C2×#66936C4semidirect
19. C2×#66932C4semidirect
36. C22×D44C2×C4semidirect
37. C22×C4×D11C2×C4semidirect
38. C22×Dic22C2×C4semidirect
60. C2×(C2×D11)⋊C4C2×C4semidirect
61. C2×(C2×D11)⋊C4C2×C4semidirect
63. C2×C4⋊Dic11C2×C4semidirect
64. C2×C4⋊Dic11C2×C4semidirect
67. C2×Dic11⋊C4C2×C4semidirect
68. C2×Dic11⋊C4C2×C4semidirect
70. C2×C4×Dic11C2×C4semidirect
145. #2315D11semidirect
382. C11#21876semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106230252
#130712142
#130696002
#130694512
#130690692
#130686012
C11×#23152
#2187611